Prediction of the quasistatic planar motion of a contacted rigid body

Planning the motion of bodies in contact requires a model of contact mechanics in order to predict sliding, rolling, and jamming. Such a model typically assumes that the bodies are rigid and that tangential forces at the contacts obey Coulomb´s law. Though, usually assumed to be constant, the static and dynamic coefficients of friction vary in space and time and are difficult to measure accurately. In this paper, we study a quasistatic, multi-rigid-body model for planar systems, in which the coefficients of friction are treated as independent variables. Our analysis yields inequalities defining regions in the space of friction coefficients for which a particular contact mode is feasible. The geometrical interpretation of these inequalities leads to a simple graphical technique to test contact mode feasibility. This technique is then used to generate a nontrivial example in which several contact modes are simultaneously feasible. Despite model ambiguity, there are factors which argue in favor of using a quasistatic, rigid-body model. This point is highlighted by the successful application of our results to the planning of two manipulation tasks